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There’s a new conference series, whose acronym is pronounced “psycho”. It’s part of the new trend toward the study of “compositionality” in many branches of thought, often but not always using category theory:

The Symposium on Compositional Structures is a new interdisciplinary series of meetings aiming to support the growing community of researchers interested in the phenomenon of compositionality, from both applied and abstract perspectives, and in particular where category theory serves as a unifying common language. We welcome submissions from researchers across computer science, mathematics, physics, philosophy, and beyond, with the aim of fostering friendly discussion, disseminating new ideas, and spreading knowledge between fields. Submission is encouraged for both mature research and work in progress, and by both established academics and junior researchers, including students.

More details below! Our very own David Corfield is one of the invited speakers.

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I want to tell you about Elmendorf’s theorem on equivariant homotopy theory. This theorem played a key role in a recent preprint I wrote with Hisham Sati and Urs Schreiber:

We figured out how to apply this theorem in mathematical physics. But Elmendorf’s theorem by itself is a gem of homotopy theory and deserves to be better known. Here’s what it says, roughly: given any G -space X , the equivariant homotopy type of X is determined by the ordinary homotopy types of the fixed point subspaces X H , where H runs over all subgroups of G . I don’t know how to intuitively motivate this fact; I would like to know, and if any of you have ideas, please comment. Below the fold, I will spell out the precise theorem, and show you how it gives us a way to define a G -equivariant version of any homotopy theory.

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Today’s installment in the ongoing project to sketch the -elephant: atomic geometric morphisms.

Cole, subduing all of Moya's men.

After Cole confided with Zeke, a missile flew by and dropped near their vicinity, making them stumble over. As the two got up, they see a whole Military aerial armada coming to the city. Cole figured immediately that it was Moya, keeping her promise about destroying the city should Cole disobey. Telling Zeke to get the Warden, the three got up and about to deal with the troops. Attacked by several choppers and soldiers, Cole managed to deal with all of these while keeping the other two safe. Cole thought that Moya would send in more troops over, which led the Warden to believe that they need to formulate a proper plan, suggesting that they head inside the Penitentiary. Cole, while inside the facility as several personnel block the paths, was contacted by Moya, whom gave him a proper warning; to surrender to them, or else the consequences will be dire. Cole told her off, and simply said that she should ready her men for him. Moya gave him until the next morning to decide. [4]

The next night at a Police Precinct in he Historic District; Cole and Harms debated on Cole turning himself over to Moya. While Cole claimed that him staying would result in many people dying Harms claimed that with Cole gone the people of Empire City would be doomed as it was Cole's presence that had kept gangs like The Dust Men, First Suns at bay. Harms then made the point of while the media so far have been able to claim that the situation in Empire City is great he claimed that eventually someone would see through the charade and that if the ECPD and Cole can hold Moya to stalemate for at least a week the situation would resolve itself. At that time a monstrous conduit named David attacked the Precinct, killing many officers and nearly killing Zeke however Cole arrives just in time to save Zeke and battle David who easily overpowers him and nearly kills him until Moya sends some soldiers who David also kills. Cole then decided to take the fight away somewhere else to prevent more people from getting hurt. David eventually catches up however and throws Cole into a building. Moya contacts Cole and tells him to get out of the building as she launches a bomb to try and take out David. Cole escapes as the building is blown up. Returning to the police station and meeting up with Zeke and the others. Cole tells them he can't stay because the "thing" was after him and he needs Zeke's apartment keys because he needs a place to sleep.

Zeke argues with Cole. Cole tells him he was saved by Moya but he can still can hear David down there scraping around, trying to escape and if it wants to kill him so bad then it can kill him alone so that no one else will get hurt. Back at the apartment Cole tearfully looked through photos of Trish.

Cole reviewing the papers given to him by Kuo.

Months later, as Cole was on his daily routine, an agent from the NSA named Lucy Kuo arrived at Empire City to meet up with him. She explained that she was fully aware of the Beast's nature and its imminent coming, also informing him of one of her associates, Dr. Prada Mens 4E2718 LZH F073A Leather Sneaker zv8pm2So
, whom previously worked with Kessler on the Ray Sphere. Offering Cole help to prepare and empower him for the Beast's advent, the only condition Kuo had was for him to come to New Marais. Cole agreed, and prepared to leave for New Marais with Kuo, along with Zeke. [1]

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